John Buridan's Sophismata

Read, "The Liar Paradox from John Buridan back to Thomas Bradwardine" (Week 10, 9 January)

  1. Postulate 2 (that every proposition signifies or means contingently or necessarily everything which follows from it contingently or necessarily) is an important postulate for Bradwardine in showing Thesis 2 (that every proposition that signifies itself not to be true or to be false, signifies itself to be true and is false). Does it sound plausible to you?

    This is certainly not how meaning is typically understood. Suppose p is necessary. Then it follows necessarily from everything. And yet we do not want to say that everything means at least partly that p. For example, 'Konstanz is in Germany' does not seem to mean that all even numbers are divisible by 2.

  2. One difference between Buridan and Bradwardine is that Buridan believed that every proposition signifies itself to be true, while Bradwardine held this only for propositions that singify themselves to be false. Do you think the generalization is much less plausible?

    It depends on one's prior views about truth. Suppose one holds that it is a "platiude" of truth that from p we can infer that p is true, and conversely; that is, that p and ''p' is true' are logically equivalent. Then if we believe the closure postulate of Bradwardine, it follows that every proposition p signifies that p is true, since it implies this. But if one has some independent story about truth as Buridan and Bradwardine do, then one may have not have this equivalence available for showing that every proposition signifies itself to be true. Indeed, the liar, call it L, is supposed to show that we do not have this equivalence since it it holds (i.e. we have that L) even though it is not true (i.e. we do not have that L is true).

  3. Why, according to Read, does Buridan's solution to paradox face a dilemma?

    The dilemma is either that the truth condition for sentences of the form ''p' is true' is either ad hoc or else generalizes to all propositions, in which case no proposition is then true. For every proposition implies its own truth, hence to show that p is true, we must show that every proposition implies its own truth, hence to show that p is true, we must show that every proposition it implies meets the suppositional requirement, including T'p', and hence that p is true. Thus, in order to show that p is true, we must show that p is true, and so the truth condition (B) "is useless as a criterion of truth in general".

    The main problem, it sems to me, is that "Buridan has claimed that for every p, p implies T'p'. Without this, (B) is not rendered useless. But this claim is supposed to be false on Buridan's view since we have that the liar, L, holds (i.e. L is false) even though it is not true, as odd as that sounds. For let L name 'L is not true'. Then L is false since it implies its own truth and falsity, and yet we do not have TL.

  4. How does Bradwardine's solution avoid Buridan's dilemma?

    The crucial difference between Buridan and Bradwardine is that Bradwardine did not hold that every proposition signifies itself to be true. Rather, this claim is restricted only to insolubilia and not for any ad hoc reason. Bradwardine proves that this is so by a relatively lengthy proof that involves no obviously ad hoc principles.